Designing a balance controller that allows a robot to perform human-like dynamic and stable walking is still a challenge. In this work, a recent theoretical framework for the balance stability analysis of bipeds is extended to two real multibody biped systems: A robot and a human subject. For each system in single support (SS) contact configuration, the threshold between balanced and falling state is calculated, resulting in the biped-specific balance stability boundary. This boundary identifies, in the state space of the center of mass (COM), all possible states that are balanced with respect to SS. A COM state outside of the boundary represents the sufficient condition for a falling state, from which a change in the current SS contact configuration is inevitable. The walking trajectories of both systems are analyzed in relationship with their respective stability boundary, in order to extrapolate useful implications on the different balance control of robot vs. human during the SS phase of walking. In addition, a metrics that quantifies the degree of instantaneous stability/instability is formulated, based on the relative distance from a COM state to the closest point on the stability boundary. The method and results proposed can help the improvement of current balance controllers in walking robots.